<html><!-- Created using the cpp_pretty_printer from the dlib C++ library.  See http://dlib.net for updates. --><head><title>dlib C++ Library - bigint_kernel_abstract.h</title></head><body bgcolor='white'><pre>
<font color='#009900'>// Copyright (C) 2003  Davis E. King (davis@dlib.net)
</font><font color='#009900'>// License: Boost Software License   See LICENSE.txt for the full license.
</font><font color='#0000FF'>#undef</font> DLIB_BIGINT_KERNEl_ABSTRACT_
<font color='#0000FF'>#ifdef</font> DLIB_BIGINT_KERNEl_ABSTRACT_

<font color='#0000FF'>#include</font> <font color='#5555FF'>&lt;</font>iosfwd<font color='#5555FF'>&gt;</font>
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../algs.h.html'>../algs.h</a>"
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../serialize.h.html'>../serialize.h</a>"
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../uintn.h.html'>../uintn.h</a>"

<font color='#0000FF'>namespace</font> dlib
<b>{</b>

    <font color='#0000FF'>class</font> <b><a name='bigint'></a>bigint</b> 
    <b>{</b>
        <font color='#009900'>/*!
            INITIAL VALUE
                *this == 0

            WHAT THIS OBJECT REPRESENTS
                This object represents an arbitrary precision unsigned integer

                the following operators are supported:
                operator +
                operator +=
                operator -
                operator -=
                operator *
                operator *=
                operator /
                operator /=
                operator %
                operator %=
                operator ==
                operator &lt;
                operator =
                operator &lt;&lt; (for writing to ostreams)
                operator &gt;&gt; (for reading from istreams)
                operator++       // pre increment
                operator++(int)  // post increment
                operator--       // pre decrement
                operator--(int)  // post decrement


                the other comparison operators(&gt;, !=, &lt;=, and &gt;=) are 
                available and come from the templates in dlib::relational_operators

            THREAD SAFETY
                bigint may be reference counted so it is very unthread safe.
                use with care in a multithreaded program

        !*/</font>

    <font color='#0000FF'>public</font>:

        <b><a name='bigint'></a>bigint</b> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #*this is properly initialized
            throws
                - std::bad_alloc
                    if this is thrown the bigint will be unusable but 
                    will not leak memory
        !*/</font>

        <b><a name='bigint'></a>bigint</b> <font face='Lucida Console'>(</font>
            uint32 value
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - value &lt;= (2^32)-1
            ensures
                - #*this is properly initialized
                - #*this == value
            throws
                - std::bad_alloc
                    if this is thrown the bigint will be unusable but 
                    will not leak memory
        !*/</font>

        <b><a name='bigint'></a>bigint</b> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> item
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #*this is properly initialized 
                - #*this == value
            throws
                - std::bad_alloc
                    if this is thrown the bigint will be unusable but 
                    will not leak memory
        !*/</font>

        <font color='#0000FF'>virtual</font> ~<b><a name='bigint'></a>bigint</b> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - all resources associated with #*this have been released
        !*/</font>

        <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the result of adding rhs to *this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #*this == *this + rhs
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect                                        
        !*/</font>

        <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            requires
                - *this &gt;= rhs
            ensures
                - returns the result of subtracting rhs from *this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - *this &gt;= rhs            
            ensures
                - #*this == *this - rhs
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the result of multiplying *this and rhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #*this == *this * rhs
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>/</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            requires
                - rhs != 0
            ensures
                - returns the result of dividing *this by rhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs != 0
            ensures
                - #*this == *this / rhs
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>%</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            requires
                - rhs != 0
            ensures
                - returns the result of *this mod rhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>%</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs != 0
            ensures
                - #*this == *this % rhs
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b> <font color='#5555FF'>&lt;</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns true if *this is less than rhs 
                - returns false otherwise
        !*/</font>

        <font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns true if *this and rhs represent the same number 
                - returns false otherwise
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #*this == rhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>


        <font color='#0000FF'>friend</font> std::ostream<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>&lt;</font><font color='#5555FF'>&lt;</font> <font face='Lucida Console'>(</font>
            std::ostream<font color='#5555FF'>&amp;</font> out,
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - the number in *this has been written to #out as a base ten number
            throws
                - std::bad_alloc
                    if this function throws then it has no effect (nothing
                    is written to out)
        !*/</font>

        <font color='#0000FF'>friend</font> std::istream<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>&gt;</font><font color='#5555FF'>&gt;</font> <font face='Lucida Console'>(</font>
            std::istream<font color='#5555FF'>&amp;</font> in,
            bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - reads a number from in and puts it into #*this 
                - if (there is no positive base ten number on the input stream ) then 
                    - #in.fail() == true
            throws
                - std::bad_alloc
                    if this function throws the value in rhs is undefined and some
                    characters may have been read from in.  rhs is still usable though,
                    its value is just unknown.
        !*/</font>


        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font><font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #*this == *this + 1 
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font><font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'><u>int</u></font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #*this == *this + 1
                - returns *this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>-</font><font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*! 
            requires
                - *this != 0
            ensures
                - #*this == *this - 1
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>-</font><font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'><u>int</u></font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - *this != 0
            ensures
                - #*this == *this - 1
                - returns *this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'><u>void</u></font> <b><a name='swap'></a>swap</b> <font face='Lucida Console'>(</font>
            bigint<font color='#5555FF'>&amp;</font> item
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - swaps *this and item
        !*/</font> 


        <font color='#009900'>// ------------------------------------------------------------------
</font>        <font color='#009900'>// ----    The following functions are identical to the above   -----
</font>        <font color='#009900'>// ----  but take uint16 as one of their arguments. They  ---
</font>        <font color='#009900'>// ----  exist only to allow for a more efficient implementation  ---
</font>        <font color='#009900'>// ------------------------------------------------------------------
</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>
            uint16 lhs,
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - lhs &lt;= 65535
            ensures
                - returns the result of adding rhs to lhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> lhs,
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs &lt;= 65535
            ensures
                - returns the result of adding rhs to lhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs &lt;= 65535
            ensures
                - #*this == *this + rhs                
                - returns #this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>
            uint16 lhs,
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - lhs &gt;= rhs 
                - lhs &lt;= 65535
            ensures
                - returns the result of subtracting rhs from lhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> lhs,
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - lhs &gt;= rhs 
                - rhs &lt;= 65535
            ensures
                - returns the result of subtracting rhs from lhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - *this &gt;= rhs 
                - rhs &lt;= 65535
            ensures
                - #*this == *this - rhs
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font> <font face='Lucida Console'>(</font>
            uint16 lhs,
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - lhs &lt;= 65535
            ensures
                - returns the result of multiplying lhs and rhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> lhs,
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs &lt;= 65535
            ensures
                - returns the result of multiplying lhs and rhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs &lt;= 65535
            ensures
                - #*this == *this * rhs
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>/</font> <font face='Lucida Console'>(</font>
            uint16 lhs,
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs != 0 
                - lhs &lt;= 65535
            ensures
                - returns the result of dividing lhs by rhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>/</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> lhs,
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs != 0 
                - rhs &lt;= 65535
            ensures
                - returns the result of dividing lhs by rhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs != 0 
                - rhs &lt;= 65535
            ensures
                - #*this == *this / rhs
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>%</font> <font face='Lucida Console'>(</font>
            uint16 lhs,
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs != 0 
                - lhs &lt;= 65535
            ensures
                - returns the result of lhs mod rhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'>const</font> bigint <b><a name='operator'></a>operator</b><font color='#5555FF'>%</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> lhs,
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs != 0 
                - rhs &lt;= 65535
            ensures
                - returns the result of lhs mod rhs
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>%</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs != 0 
                - rhs &lt;= 65535
            ensures
                - #*this == *this % rhs
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>


        <font color='#0000FF'>friend</font> <font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b> <font color='#5555FF'>&lt;</font> <font face='Lucida Console'>(</font>
            uint16 lhs,
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - lhs &lt;= 65535
            ensures
                - returns true if lhs is less than rhs 
                - returns false otherwise
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b> <font color='#5555FF'>&lt;</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> lhs,
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs &lt;= 65535
            ensures
                - returns true if lhs is less than rhs 
                - returns false otherwise
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> lhs,
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs &lt;= 65535
            ensures
                - returns true if lhs and rhs represent the same number 
                - returns false otherwise
        !*/</font>

        <font color='#0000FF'>friend</font> <font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            uint16 lhs,
            <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - lhs &lt;= 65535
            ensures
                - returns true if lhs and rhs represent the same number 
                - returns false otherwise
        !*/</font>

        bigint<font color='#5555FF'>&amp;</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
            uint16 rhs
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - rhs &lt;= 65535
            ensures
                - #*this == rhs
                - returns #*this
            throws
                - std::bad_alloc
                    if this function throws then it has no effect
        !*/</font>

    <b>}</b>;   
   
    <font color='#0000FF'>inline</font> <font color='#0000FF'><u>void</u></font> <b><a name='swap'></a>swap</b> <font face='Lucida Console'>(</font>
        bigint<font color='#5555FF'>&amp;</font> a, 
        bigint<font color='#5555FF'>&amp;</font> b 
    <font face='Lucida Console'>)</font> <b>{</b> a.<font color='#BB00BB'>swap</font><font face='Lucida Console'>(</font>b<font face='Lucida Console'>)</font>; <b>}</b>   
    <font color='#009900'>/*!
        provides a global swap function
    !*/</font>

    <font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> item, 
        std::istream<font color='#5555FF'>&amp;</font> in
    <font face='Lucida Console'>)</font>;   
    <font color='#009900'>/*!
        provides serialization support 
    !*/</font>

    <font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b> <font face='Lucida Console'>(</font>
        bigint<font color='#5555FF'>&amp;</font> item, 
        std::istream<font color='#5555FF'>&amp;</font> in
    <font face='Lucida Console'>)</font>;   
    <font color='#009900'>/*!
        provides deserialization support 
    !*/</font>

    <font color='#0000FF'>inline</font> <font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b><font color='#5555FF'>&gt;</font>  <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> a, <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> b<font face='Lucida Console'>)</font> <b>{</b> <font color='#0000FF'>return</font> b <font color='#5555FF'>&lt;</font> a; <b>}</b> 
    <font color='#0000FF'>inline</font> <font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b><font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> a, <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> b<font face='Lucida Console'>)</font> <b>{</b> <font color='#0000FF'>return</font> <font color='#5555FF'>!</font><font face='Lucida Console'>(</font>a <font color='#5555FF'>=</font><font color='#5555FF'>=</font> b<font face='Lucida Console'>)</font>; <b>}</b>
    <font color='#0000FF'>inline</font> <font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b><font color='#5555FF'>&lt;</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> a, <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> b<font face='Lucida Console'>)</font> <b>{</b> <font color='#0000FF'>return</font> <font color='#5555FF'>!</font><font face='Lucida Console'>(</font>b <font color='#5555FF'>&lt;</font> a<font face='Lucida Console'>)</font>; <b>}</b>
    <font color='#0000FF'>inline</font> <font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b><font color='#5555FF'>&gt;</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> a, <font color='#0000FF'>const</font> bigint<font color='#5555FF'>&amp;</font> b<font face='Lucida Console'>)</font> <b>{</b> <font color='#0000FF'>return</font> <font color='#5555FF'>!</font><font face='Lucida Console'>(</font>a <font color='#5555FF'>&lt;</font> b<font face='Lucida Console'>)</font>; <b>}</b>
<b>}</b>

<font color='#0000FF'>#endif</font> <font color='#009900'>// DLIB_BIGINT_KERNEl_ABSTRACT_
</font>

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